Supplementary Information for
Supplementary Information for Electronic Structure and Bonding in Co-based Single and Mixed Valence Oxides. A Quantum Chemical Perspective
Vijay Singh and Dan Thomas Major* Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry and the Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, RamatGan 52900, Israel *
Electronic mail: [email protected] 1
Bar-Ilan University
S1
Figure S1. Possible magnetic structures for Co2O3 such as antiferromagnetic (AFM) configuration where we include (a) A-type, (b) C-type, and (c) G-type AFM ordering, ferromagnetic (FM) configuration (d) where all the spins align in one direction, and also (e) a configuration where an unequal number of up and down magnetic atoms are present in the unit cell.
S2
Figure S2. (a) The local magnetic moment on each Co3+ ion for different sets of magnetic configuration, such as A-type, Ferri, C-type, G-type and FM. We highlighted the low energy Ferri (green bar) and C-type (red bar) configurations to make them distinguishable from that of the high energy configurations. The results are shown for a larger volume of 318.05 Å3 of the Co2O3 unit cell. (b) The total magnetic moment of the Co2O3 unit cell for different sets of magnetic configuration, such as A-type, Ferri, C-type, G-type and FM.
(b)
Total Magnetic Moment (µB/f.u.
(a)
4 3 2 1 0
FM
C-type G-type Ferri
S3
A-type
Figure S3. The change in magnetic moment per Co3+ ion (i.e. low spin (LS) to high-spin (HS) transformation) as a function of unit cell volume change.
S4
Figure S4. The partial densities of states for the A-type magnetic structure of Co2O3 in a larger volume phase, where the Co3+ ions are in a HS state.
S5
Figure S5. Model magnetic structure for Co3O4 (a) and CoO (b). Note that Co2O3 is diamagnetic in its ground state.
S6
Figure S6. The phase diagram for the ground state of (a) Co3O4 (adopted from Quia et al.1) (b) Co2O3, and (c) CoO as a function of the Hubbard U parameter. The change in the magnetic moment per Co site and the band gap in the antiferromagnetic phase as a function of U are shown.
S7
Figure S7. The partial densities of states for the Co2+ and Co3+ions in Co3O4 using (a) PBE, PBE+U with two sets of Ueff: (b) 2.0 and 1.0 eV and (c) 4.4 and 6.7 eV, and the HSE06 functional with (d) 5% and (e) 25% short range HF exact exchange.
S8
Figure S8. The partial densities of states for Co2O3 using (a) PBE, PBE+U with Ueff (Co3+) equals (b) 3 eV and (c) 7 eV, and the HSE06 functional with (d) 5% and (e) 25% short range HF exact exchange.
S9
Figure S9. The partial densities of states for CoO using (a) PBE, PBE+U with Ueff (Co2+) equals (b) 2 eV and 8 eV (c), and the HSE06 functional with (d) 5% and (e) 25% short range HF exchange.
S10
Figure S10. The total density of states for CoO, Co3O4, and Co2O3 using (b) HSE06 (α = 25%), (e) PBE, and (h) PBE functionals, respectively. Additionally, the total density of states for one electron addition and subtraction i.e. (N+1 and N-1, where N is the number of valence electrons in the respective unit cells) is also shown in (a and c), (d and f), and (g and i) for CoO, Co3O4 and Co2O3, respectively.
S11
Figure S11. Comparison of the global crystal coordinates and the local coordinates of the associated ligands (x, y, z) for various metal ions. Co3+ is in an octahedral complex in (a) Co3O4 and (b) Co2O3, and Co2+ is in an octahedral and tetrahedral complex in (c) CoO and (d) Co3O4, respectively.
S12
Figure S12. A comparison of the off-site COHPs and ICOHPs (red) per bond for nearest neighbor of Co3+ (3d-eg and t2g) or Co2+ (3d-eg and t2g) and O (2p) for each cobalt oxide material: Co2O3 (a), Co3O4 (b, d), and CoO (c) in both spin-up (top panel) and spin-down (bottom panel) channels. All energies are relative to the Fermi energy.
S13
Figure S13. A comparison of off-site COHPs and ICOHPs (red) per bond for nearest neighbors of Co2+ - Co2+ for CoO (a, c) and Co3O4 (b, d) in both spin-up (top panel) and spin-down (bottom panel) channels. All energies are relative to the Fermi energy.
S14
Figure S14. A comparison of off-site COHPs and ICOHPs (red) per bond for nearest neighbors of Co3+ - Co3+ for Co2O3 (a, c) and Co3O4 (b, d) in both spin-up (top panel) and spin-down (bottom panel) channels. All energies are relative to the Fermi energy.
S15
Figure S15. Off-site COHPs and ICOHPs (red) per bond for nearest neighbors of Co2+ - Co3+ for Co3O4 in both spin-up (a) and spin-down (b) channels. All energies are relative to the Fermi energy.
S16
Figure S16. Off-site COHPs and ICOHPs (red) per bond for nearest neighbors of (a) spin-up Co2+-O, (b) spindown Co2+-O, (c) spin-up Co3+-O, and (d) spin-down Co3+-O. All energies are relative to the Fermi energy.
(a
(c)
(b)
(d)
S17
Figure S17. A schematic representation of defect tolerant analysis in (a) CoO, (b) Co2O3, and (c) Co3O4, based on Zakutayev et al.2
(a)
(c)
(b)
S18
Figure S18. A schematic depiction of σ and π bonds in an octahedral complex ion. The ligands are numbered from 1 to 6.
S19
Table S1. Symmetry classification of molecular orbitals for Oh symmetry (the ligands are numbered according to Figure S18).3
Symmetry
Orbital of the
Orbital of the ligands
MO’s
central ion σ orbitals
π orbitals
a1g
4s
1/√6 (z1 + z2 + z3+ z4 + z5 + z6)
t1u
4px
1/√2 (z1 –z4)
½ (y2 + x3 – x5 –y6)
4py
1/√2 (z2 – z5)
½ (x1 + y3 –y4 –x6)
4pz
1/√2 (z3 – z6)
½ (y1 + x2 –x4 –y5)
3dx2-y2
½ ( z1 –z2 + z4 - z5)
3dz2
1/√12 (z1 + z2 - 2z3+ z4 + z5– 2z6)
eg
t2g
sa1g, σa1g
deg, σeg
3dxy
½ ( x1 + y2 –y4 –x5)
3dxz
½ (y1 + x3 + x4 + y6)
3dyz
½ (x2 + y3 + y5 + x6)
S20
pt1u, σt1u, pt1u, πt1u
dt2g, πt2g
References (1)
Qiao, L.; Xiao, H.; Meyer, H.; Sun, J.; Rouleau, C.; Puretzky, A.; Geohegan, D.; Ivanov, I.; Yoon, M.;
Weber, W., Journal of Materials Chemistry C 2013, 1, 4628-4633. (2)
Zakutayev, A.; Caskey, C. M.; Fioretti, A. N.; Ginley, D. S.; Vidal, J.; Stevanovic, V.; Tea, E.; Lany, S.,
The Journal of Physical Chemistry Letters 2014, 5, 1117-1125. (3)
Schläfer, H. L.; Gliemann, G., Basic principles of ligand field theory. Wiley-Interscience: 1969.
S21
Vijay Singh and Dan Thomas Major* Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry and the Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, RamatGan 52900, Israel *
Electronic mail: [email protected] 1
Bar-Ilan University
S1
Figure S1. Possible magnetic structures for Co2O3 such as antiferromagnetic (AFM) configuration where we include (a) A-type, (b) C-type, and (c) G-type AFM ordering, ferromagnetic (FM) configuration (d) where all the spins align in one direction, and also (e) a configuration where an unequal number of up and down magnetic atoms are present in the unit cell.
S2
Figure S2. (a) The local magnetic moment on each Co3+ ion for different sets of magnetic configuration, such as A-type, Ferri, C-type, G-type and FM. We highlighted the low energy Ferri (green bar) and C-type (red bar) configurations to make them distinguishable from that of the high energy configurations. The results are shown for a larger volume of 318.05 Å3 of the Co2O3 unit cell. (b) The total magnetic moment of the Co2O3 unit cell for different sets of magnetic configuration, such as A-type, Ferri, C-type, G-type and FM.
(b)
Total Magnetic Moment (µB/f.u.
(a)
4 3 2 1 0
FM
C-type G-type Ferri
S3
A-type
Figure S3. The change in magnetic moment per Co3+ ion (i.e. low spin (LS) to high-spin (HS) transformation) as a function of unit cell volume change.
S4
Figure S4. The partial densities of states for the A-type magnetic structure of Co2O3 in a larger volume phase, where the Co3+ ions are in a HS state.
S5
Figure S5. Model magnetic structure for Co3O4 (a) and CoO (b). Note that Co2O3 is diamagnetic in its ground state.
S6
Figure S6. The phase diagram for the ground state of (a) Co3O4 (adopted from Quia et al.1) (b) Co2O3, and (c) CoO as a function of the Hubbard U parameter. The change in the magnetic moment per Co site and the band gap in the antiferromagnetic phase as a function of U are shown.
S7
Figure S7. The partial densities of states for the Co2+ and Co3+ions in Co3O4 using (a) PBE, PBE+U with two sets of Ueff: (b) 2.0 and 1.0 eV and (c) 4.4 and 6.7 eV, and the HSE06 functional with (d) 5% and (e) 25% short range HF exact exchange.
S8
Figure S8. The partial densities of states for Co2O3 using (a) PBE, PBE+U with Ueff (Co3+) equals (b) 3 eV and (c) 7 eV, and the HSE06 functional with (d) 5% and (e) 25% short range HF exact exchange.
S9
Figure S9. The partial densities of states for CoO using (a) PBE, PBE+U with Ueff (Co2+) equals (b) 2 eV and 8 eV (c), and the HSE06 functional with (d) 5% and (e) 25% short range HF exchange.
S10
Figure S10. The total density of states for CoO, Co3O4, and Co2O3 using (b) HSE06 (α = 25%), (e) PBE, and (h) PBE functionals, respectively. Additionally, the total density of states for one electron addition and subtraction i.e. (N+1 and N-1, where N is the number of valence electrons in the respective unit cells) is also shown in (a and c), (d and f), and (g and i) for CoO, Co3O4 and Co2O3, respectively.
S11
Figure S11. Comparison of the global crystal coordinates and the local coordinates of the associated ligands (x, y, z) for various metal ions. Co3+ is in an octahedral complex in (a) Co3O4 and (b) Co2O3, and Co2+ is in an octahedral and tetrahedral complex in (c) CoO and (d) Co3O4, respectively.
S12
Figure S12. A comparison of the off-site COHPs and ICOHPs (red) per bond for nearest neighbor of Co3+ (3d-eg and t2g) or Co2+ (3d-eg and t2g) and O (2p) for each cobalt oxide material: Co2O3 (a), Co3O4 (b, d), and CoO (c) in both spin-up (top panel) and spin-down (bottom panel) channels. All energies are relative to the Fermi energy.
S13
Figure S13. A comparison of off-site COHPs and ICOHPs (red) per bond for nearest neighbors of Co2+ - Co2+ for CoO (a, c) and Co3O4 (b, d) in both spin-up (top panel) and spin-down (bottom panel) channels. All energies are relative to the Fermi energy.
S14
Figure S14. A comparison of off-site COHPs and ICOHPs (red) per bond for nearest neighbors of Co3+ - Co3+ for Co2O3 (a, c) and Co3O4 (b, d) in both spin-up (top panel) and spin-down (bottom panel) channels. All energies are relative to the Fermi energy.
S15
Figure S15. Off-site COHPs and ICOHPs (red) per bond for nearest neighbors of Co2+ - Co3+ for Co3O4 in both spin-up (a) and spin-down (b) channels. All energies are relative to the Fermi energy.
S16
Figure S16. Off-site COHPs and ICOHPs (red) per bond for nearest neighbors of (a) spin-up Co2+-O, (b) spindown Co2+-O, (c) spin-up Co3+-O, and (d) spin-down Co3+-O. All energies are relative to the Fermi energy.
(a
(c)
(b)
(d)
S17
Figure S17. A schematic representation of defect tolerant analysis in (a) CoO, (b) Co2O3, and (c) Co3O4, based on Zakutayev et al.2
(a)
(c)
(b)
S18
Figure S18. A schematic depiction of σ and π bonds in an octahedral complex ion. The ligands are numbered from 1 to 6.
S19
Table S1. Symmetry classification of molecular orbitals for Oh symmetry (the ligands are numbered according to Figure S18).3
Symmetry
Orbital of the
Orbital of the ligands
MO’s
central ion σ orbitals
π orbitals
a1g
4s
1/√6 (z1 + z2 + z3+ z4 + z5 + z6)
t1u
4px
1/√2 (z1 –z4)
½ (y2 + x3 – x5 –y6)
4py
1/√2 (z2 – z5)
½ (x1 + y3 –y4 –x6)
4pz
1/√2 (z3 – z6)
½ (y1 + x2 –x4 –y5)
3dx2-y2
½ ( z1 –z2 + z4 - z5)
3dz2
1/√12 (z1 + z2 - 2z3+ z4 + z5– 2z6)
eg
t2g
sa1g, σa1g
deg, σeg
3dxy
½ ( x1 + y2 –y4 –x5)
3dxz
½ (y1 + x3 + x4 + y6)
3dyz
½ (x2 + y3 + y5 + x6)
S20
pt1u, σt1u, pt1u, πt1u
dt2g, πt2g
References (1)
Qiao, L.; Xiao, H.; Meyer, H.; Sun, J.; Rouleau, C.; Puretzky, A.; Geohegan, D.; Ivanov, I.; Yoon, M.;
Weber, W., Journal of Materials Chemistry C 2013, 1, 4628-4633. (2)
Zakutayev, A.; Caskey, C. M.; Fioretti, A. N.; Ginley, D. S.; Vidal, J.; Stevanovic, V.; Tea, E.; Lany, S.,
The Journal of Physical Chemistry Letters 2014, 5, 1117-1125. (3)
Schläfer, H. L.; Gliemann, G., Basic principles of ligand field theory. Wiley-Interscience: 1969.
S21
